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AP EAMCET202021 Sep 2020Morning ShiftMathematicsVector AlgebraActual

If ( a =2 i -3 j -4 k , b = i +4 j -2 k ), ( c =3 i - j +4 k ) then, ( [ array lll a b & b c c a array ]= )

Options

  1. A4900
  2. B6400
  3. C8100
  4. D12100

Correct answer

D. 12100

Step-by-step solution

Given vector ( aligned & a =2 i -3 j -4 k & b = i +4 j -2 k and c =3 i - j +4 k aligned ) and as we know that ( [ array lll a b & b c & c a array ]= [ array lll a & b & c array ]^2 ) and ( [ array lll a & b & c array ]= | array ccc 2 & -3 & -4 1 & 4 & -2 3 & -1 & 4 array | ) ( aligned & =2(16-2)+3(4+6)-4(-1-12) & =28+30+52=110 aligned ) ( [ array lll a b & b c & c a array ]= [ array lll a & b & c array ]^2=(110)^2=12100 ) Hence, option (d) is correct.

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